Question

a certain standardized test measures students knowledge in english and math. the english and math scores for 10 randomly selected students are given in the table.
using technology, what is the equation for the least - squares regression line?
○ \\( \hat { y } = 180.2 + 0.68 x \\)
○ \\( \hat { y } = 0.68 + 180.2 x \\)
○ \\( \hat { y } = - 124.1 + 1.22 x \\)
○ \\( \hat { y } = 1.22 - 124.1 x \\)

Explanation:

Step1: Recall the form of the least - squares regression line

The least - squares regression line has the form \(\hat{y}=a + bx\), where \(a\) is the y - intercept and \(b\) is the slope.

Step2: Analyze the slope

The slope \(b\) represents the change in \(y\) (math score) for a unit change in \(x\) (English score). A positive slope indicates a positive correlation.

Step3: Check the y - intercept

The y - intercept \(a\) is the value of \(\hat{y}\) when \(x = 0\).

Step4: Use technology (e.g., a graphing calculator)

Input the \(x\) (English) and \(y\) (math) data points into a graphing calculator. Calculate the least - squares regression line.
When we calculate the least - squares regression line for the given data (using a graphing calculator or statistical software), we find that the equation is \(\hat{y}=- 124.1+1.22x\)

Answer:

\(\hat{y}=-124.1 + 1.22x\) (the third option)